RGG FAQ Part 1 Section 10
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Go is always a struggle of territory against central influence. Territory is most often built on the third line from the edge, whereas central influence most often arises from stones on the fourth line.
The 19×19 board is the one where the balance between third line territory and fourth line influence is best. Refer to the following diagram for explanation of this fact. (The low white position in the corner is due to the necessity of having as many black as white stones on the board, and the center is missing for the jigo.)
Boards with odd length are much preferred over boards with even length because the central point ('tengen' in Japanese) can serve Black very well to counter a white mirror mimic Go strategy. On a 20×20 board, mirror mimic games tend to become very complicated for Black.
Besides, the central point of the board also has some mystic meaning in Go. Its absence on a board with even length would be regrettable.